The document is a mathematics tutorial focused on algebraic concepts, including operations on expressions, simplification, factoring, radical form conversion, and evaluating expressions. It consists of multiple questions that require performing operations, reducing fractions, and identifying polynomials among others. The tutorial likely serves as a practice tool for students to sharpen their skills in algebra.

1. Module 1 Check Your Understanding
Discussion Board Tutorial
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Question
1.

2. Perform the indicated operations and simplify. (5x – 3y)2
a. 25x2 – 30xy + 9y2
b. 25x2 – 9y2
c. 25x2 – 30xy – 9y2
d. 25x2 + 9y2
2.
Change to radical form. Do not simplify.
a.
b.
c.
d.
3.
Reduce the fraction to lowest terms.
a.
b.
c.
d.
4.
Subtract 2a2 + 6a – 6 from 7a2 – 10a – 7.
a. 5a2 – 4a – 13
b. 5a2 – 4a – 1
c. 5a2 – 16a – 1
d. 5a2 – 16a – 13
5.
Write the expression in simplified radical form.
a.
b.
c.
d.
6.

3. Evaluate.
a. -
b.
c. 2
d. –2
7.
Factor completely, relative to the integers. x2 + 7x + 8x + 56
a. (x – 7)(x – 8)
b. (x + 7)(x – 8)
c. (x + 1)(x + 56)
d. (x + 7)(x + 8)
8.
Simplify. (2a–7b2)–5
a.
b.
c.
d.
9.
Write the expression in simplified radical form.
a.
b.
c.
d.
10.
Factor completely, relative to the integers. 9x2 + 12x + 4
a. (3x + 2)2
b. (3x – 2)(3x + 2)
c. (9x + 2)(x + 2)
d. (3x + 1 )(3x + 4)
11.
Reduce the fraction to lowest terms.

4. a.
b.
c.
d.
12.
Add 2x2 – 8x – 5 and 5x2 – 4x – 10.
a. 7x2 – 12x – 15
b. 7x2 – 12x + 5
c. 7x2 + 4x – 15
d. 7x2 + 4x + 5
13.
Simplify and express your answer using positive exponents
only.
a.
b.
c. m24
d. m11
14.
Evaluate the expression if it is a real number.
a. -3
b. -9
c. -27
d. -15
15.
Perform the indicated operations and reduce to lowest terms.
a.
b.
c.
d.

5. 16.
Change to radical form. Do not simplify.
a.
b.
c.
d.
17.
Evaluate. (–2)–2
a. 1/4
b. 1
c. 2
d. 4
18.
Perform the indicated operations and simplify. 5x – 4x[8 – 3(x –
2)]
a. 6x2 – 3x
b. 12x2 – 51x
c. 12x2 + 5x + 6
d. 12x2 + 5x – 6
19.
Which of the following is not a polynomial?
a. 4x3 + 5x – 1
b. 2x –
c. 3xy2 + xy
d. 24
20.
Evaluate the expression if it is a real number.
a. 32
b. 4
c. 64
d. 8

6. 21.
Simplify and express your answer using positive exponents
only. -1/x-60
a. x4
b. –x60
c.
d.
22.
Perform the indicated operations and reduce to lowest terms.
a.
b.
c.
d.
23.
Write the expression in simplified radical form.
a.
b.
c.
d.
24.
Write the expression in simplified radical form.
a.
b.
c.
d.
25.
Evaluate. 34
a. 81
b. 120
c. 24
d. 3

7. 26.
Factor completely, relative to the integers. 6b4 – 18b3 – 60b2
a. 6b2(b + 2)(b – 5)
b. 6b2(b – 2)(b + 5)
c. 6(b2 + 2)(b2 – 5)
d. b2(2b + 5)(3b + 10)
27.
Perform the indicated operations and reduce to lowest terms.
a. -
b.
c.
d. 1
28.
Factor completely, relative to the integers. 49a2b – b3
a. (7a + b2)(7a – b)
b. b(7a + b)(7a – b)
c. b(7a – b)2
d. Prime, doesn't factor
29.
Simplify and express your answer using positive exponents
only. (4w10)(7w6)(2w)
a. 13w60
b. 13w17
c. 56w60
d. 56w17
30.
Change to rational exponent form. Do not simplify.
a.
b.
c.

8. d.
31.
Evaluate. (–5)4
a. 225
b. 125
c. 625
d. 25
32.
Write 6,640,000 in scientific notation.
a. 6.64 x 106
b. 6.64 x 105
c. 66.4 x 106
d. 66.4 x 105
33.
Factor completely, relative to the integers. x2 + 36
a. (x – 6)(x + 6)
b. (x + 1)(x + 36)
c. (x + 6)2
d. Prime
34.
Perform the indicated operations and reduce to lowest form.
Represent any compound fractions as simple fractions reduced
to lowest terms.
a.
b.
c.
d.

9. 0
0
0
0
0
0
S
tart
0
0
0
0
0
Fini
s
h
0
0
0

10. 0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0

11. 0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0

12. 0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0

13. 0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0

14. 0
0
0
0
0
0
0
0
0
0
0
0
0